Find the height $h$ of a pyramid if side $a = 22.4 cm$ and slant height $s = 90.6 cm$ .

Answer

$89.9051 cm$

Explanation

To find height $h$ use Pythagorean Theorem:

h^{2} + \frac{a ^{2}}{4} = s^{2}

After substituting $a = 22.4 cm$ and $s = 90.6 cm$ we have:

h^{2} + \frac{( 22.4 cm ) ^{2}}{4} = (90.6 cm)^{2}

h^{2} + \frac{501.76 cm ^{2}}{4} = (90.6 cm)^{2}

h^{2} + 125.44 cm^{2} = (90.6 cm)^{2}

h^{2} = 8208.36 cm^{2} - 125.44 cm^{2}

h^{2} = 8082.92 cm^{2}

h = 8082.92 cm^{2}

h = 89.9051 cm

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Find the height h of a pyramid if side a=22.4cm and slant height s=90.6cm.

89.9051cm

Find the height $h$ of a pyramid if side $a = 22.4 cm$ and slant height $s = 90.6 cm$ .

$89.9051 cm$